Dispersion engineering of Quantum Cascade Lasers frequency combs

Gustavo Villares,a Sabine Riedi, Johanna Wolf, Dmitry Kazakov, Martin J. Suess, Mattias Beck, and Jerome Faistb

Institute for Quantum Electronics, ETH Zurich, Switzerland

Quantum cascade lasers are compact sources capable of generating frequency combs. Yet keycharacteristics - such as optical bandwidth and power-per-mode distribution - have to be improvedfor better addressing spectroscopy applications. Group delay dispersion plays an important role inthe comb formation. In this work, we demonstrate that a dispersion compensation scheme basedon a Gires-Tournois Interferometer integrated into the QCL-comb dramatically improves the comboperation regime, preventing the formation of high-phase noise regimes previously observed. Thecontinuous-wave output power of these combs is typically > 100 mW with optical spectra centeredat 1330 cm−1 (7.52 µm) with ∼ 70 cm−1 of optical bandwidth. Our findings demonstrate thatQCL-combs are ideal sources for chip-based frequency comb spectroscopy systems.

a gustavo.villares@phys.ethz.chb jfaist@phys.ethz.ch

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Optical frequency combs have revolutionized the fields of high-resolution and precision atomic spectroscopy dueto their high coherence, wide spectral bandwidth and absolute traceability [1, 2]. Initially developed in the near-infrared (NIR) spectral region, frequency combs are now being extended to other parts of the spectrum. In particular,extending the spectral range of frequency combs into the mid-infrared (MIR) and terahertz (THz) regions will open newpossibilities in the fields of frequency metrology, molecular spectroscopy, chemical analysis and medical diagnosis [3],as the fundamental roto-vibrational absorption lines of a variety of molecules lie in this spectral region.

Different schemes have been investigated for generating MIR frequency combs. A well-established approach consistsof transferring frequency combs from the near-infrared region into the MIR region through nonlinear processes using,for example, optical parametric oscillators [4, 5] or difference frequency generation in fiber-based NIR combs [6–8].Other examples include MIR combs generated by transition metals incorporated into chalcogenide hosts [9, 10] orThulium-doped silica fiber lasers [11]. These sources are now well-established and applications such as MIR high-resolution spectroscopy are possible. These methods guarantee good spectral coverage and coherence, but usuallyrequire delicate experimental set-ups with large footprints.

Significant effort has been recently made for achieving chip-based MIR frequency combs. Microresonator frequencycombs (Kerr-combs) have been significantly improved [12–15] and have been extended to the MIR region [16–18].Although Kerr-combs can be produced in different material platforms, they still require a high-power continuouswave (CW) laser as well as an evanescent coupling system, especially difficult to achieve in the MIR and THz regions.

Quantum cascade lasers (QCL) have proven to be semiconductor lasers capable of generating comb radiation in theMIR and THz regions [19–21]. As the comb formation takes place directly in the QCL active region, QCL frequencycombs (QCL-combs) offer the unique possibility of a completely integrated chip-based system capable of performingbroadband high-resolution spectroscopy. Such a compact system is ideal for applications requiring the detection ofseveral different molecules masked by a complex background matrix.

Meanwhile, dual-comb spectroscopy using QCL-combs has been demonstrated [22] and a theoretical descriptionof the comb formation has recently been developed [23, 24]. However, key characteristics of QCL-combs - such asoptical bandwidth and power-per-mode distribution - still need to be improved in order to better address spectroscopyapplications.

Group delay dispersion (GDD) plays an important role in the formation of QCL-combs [19, 20, 24]. In thiswork, we investigate a scheme for controlling the dispersion in MIR QCL-combs. We demonstrate that a dispersioncompensation scheme based on a Gires-Tournois Interferometer [25] (GTI) directly integrated into the QCL-combimproves the comb performance. In particular, we show that the current range where the comb operates increases,effectively suppressing the high-phase noise regime usually observed in QCL-combs [19, 20, 22, 26, 27]. Additionally,the power-per-mode distribution is improved. The CW output power of these combs is typically > 100 mW and theiroptical spectra are centered at 1330 cm−1 (7.52 µm) with ∼ 70 cm−1 of optical bandwidth.

A. Integrated Gires-Tournois interferometer for dispersion compensation

Optical frequency combs are generated when the different longitudinal modes of a laser are locked in phase [1, 2],creating an array of equidistantly spaced phase-coherent modes. As demonstrated previously [19, 28], broadband QCLscan achieve frequency comb operation by using four-wave-mixing (FWM) as a phase-locking mechanism. Combinedwith the short gain recovery time (τ ' 0.3 ps) inherent of intersubband transitions, QCL-combs show a phase signaturecomparable to a frequency-modulated laser [19, 23].

Efficient FWM process only occurs if the phase-mismatch ∆k between the modes involved in the FWM processnearly vanishes [29, 30], i.e.

∆k =n4ω4 + n3ω3 − n2ω2 − n1ω1

c' 0

where ωi are the different mode frequencies involved in the FWM process and ni is the effective mode index at thefrequency ωi. As the phase-mismatch condition depends on the effective mode indeces at different optical frequencies,a precise control of the dispersion of the laser is needed. More precisely, the phase-mismatch ∆k in a QCL can beexpressed as

∆k = ∆kmat + ∆kwg + ∆kgain + ∆kNL

where ∆kmat, ∆kwg and ∆kgain represent the phase-mismatch introduced by the material, by the laser waveguideand by the gain, respectively. The term ∆kNL represents the phase-mismatch that can be introduced by self-phaseand cross-phase modulation [30]. The advantage of QCLs regarding the generation of frequency combs is that thesecontributions can be tailored by design. As already shown experimentally in single-mode fibers [30–32] and alsoin Kerr-combs [14, 15], the FWM process starts to be efficient when working close to the zero-dispersion region.

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FIG. 1. Standard QCL-comb performances. a Set-up used for characterizing the QCL-comb. The optical spectrum is measuredwith a FTIR (Bruker IFS 66/S, 0.12 cm−1 resolution). A bias-tee is inserted between the low-noise current driver (WavelengthElectronics) and the QCL-comb. The radio-frequency (RF) port of the bias-tee is connected to a Spectrum Analyser (Rhode& Schwarz FSU50). BS.: beam-splitter. FTIR: Fourier Transform Infrared Spectrometer. b Power-current-voltage of a QCL-comb (4.5 mm long, standard HR coating on the back facet, episide-down mounted on AlN submount) in CW operation atdifferent temperatures. Single-mode, comb and high-phase noise regimes are highlighted. c Electrical RF spectra acquired atT = -15 C at different values of current, measured with a spectrum analyser (span = 50 MHz, resolution bandwidth (RBW)= 30 kHz, acquisition time = 20 ms). The RF spectra are centered at 9.95 GHz, corresponding to the RF beatnote created bya 4.5 mm long device. Comb and high-phase noise regimes are highlighted. d Optical spectra acquired at T = -15 C at thesame values of current as in Fig. 1c and measured with a FTIR (0.12 cm−1 resolution). The QCL-comb spectrum is centeredat 1325 cm−1 and spans over 60 cm−1 in the comb regime.

In this region, the different contributions ∆kmat, ∆kwg, ∆kgain and ∆kNL, which may assume positive or negativevalues, start to be of comparable magnitude. One can therefore design one of the contributions to cancel the othersand satisfy the phase-matching condition, thus enhancing the FWM process [33]. The enhancement of the FWMefficiency is detrimental in the case of multichannel optical telecommunications systems, where high input powersintroduce crosstalk between the different channels due to FWM [34], but is an advantage in combs phase-locked byFWM [14, 15].

On this basis, we design the QCL-combs in the regime where the GDD is nearly zero. As QCLs are basedon heterostructures where the composition can be tailored, the material dispersion can be controlled. The MIRQCL-combs used in this study are based on In0.60Ga0.40As/In0.355Al0.665As heterostructures grown on InP. Also, weoptimize the mode profile in the waveguide for reducing the contribution of waveguide dispersion. This optimization isachieved by adjusting the number of periods of the QC structure and the doping profile of the InP cladding layer grownon top of the active region. Finally, the laser gain design is based on 2 different bound-to-continuum strain-balanceddesigns in the active regions, which are designed in order to minimize the dispersion introduced by the gain [19].

Fig. 1 shows the typical performance of MIR QCL-combs engineered in order to operate near the zero-dispersionregion. The comb optical spectra and repetition frequency are measured simultaneously (c.f. Fig. 1a and methods).The device operates at room-temperature emitting > 10 mW of output power in CW operation (c.f. Fig. 1b). Moreimportantly, we also report in Fig. 1b the three different regimes that are typically observed in QCL-combs [19, 20, 22,26, 27]. The laser emits single-mode radiation after the laser threshold. After a second threshold, the laser operatesin a comb regime. Finally, at higher values of current, we observe a third regime, called high phase-noise regimehereafter. These three different regimes are well observed when measuring the radio-frequency (RF) beatnote and

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FIG. 2. GTI mirrors for dispersion compensation. a SEM picture of a cross section parallel to the laser ridge of the QCL-comb,which is coated with a GTI mirror. The upper left side shows the laser active region. The different layers of the GTI mirrorcan be observed as the vertical lines on the right side of the picture. b Schematic view of GTI mirror coated either on theback-facet of a QCL-comb or on a substrate (InP, 320 µm thick) to be used for dispersion characterization. The GTI actsas a high-relectivity mirror but adds a frequency dependent group delay, therefore introducing dispersion. c Set-up used forthe characterization of the dispersion introduced by the GTI mirror. The GTI mirrors coated on a substrate are measuredin reflection on the sample compartment of the FTIR (see Appendix A). DUT: device under test. d Measured and simulatedvalue of the GDD created by a GTI mirror. The GDD is measured over a wide spectral range in order to observe the GDDoscillations introduced by the GTI. The spectral region where the QCL-comb operates is highlighted. The GDD of a standardHR coating (300 nm of Al2O3, 150 nm of gold) is also represented. Inset: Zoom on the spectral region where the QCL-comboperates, showing the negative GDD introduced due to the presence of the residual absorption of SiO2.

the optical spectrum, as shown in Fig. 1c and Fig. 1d, respectively. In the single-mode regime, no RF beatnote isobserved. The comb regime is characterized by a single low-noise beatnote, corresponding to a regime where all themodes are phase-locked [19] and equidistantly spaced [22]. Finally, the high-phase noise regime is identified by abroader beat note. In this high-phase noise noise regime, both amplitude and phase noise of the laser are significantlyhigher then in the comb regime [27]. Comb operation is therefore achieved only for a narrow range of the dynamicrange of the laser operation. Moreover, comb operation is observed in regions relatively close to laser threshold, whereboth output power and optical spectral bandwidth are small compared to roll-over, as shown in Fig. 1b. Finally, wealso observe in Fig. 1d that the power distribution between the modes is highly inhomogeneous, which is not optimalfor spectroscopy applications based on frequency combs [22].

In order to further control the dispersion of QCL-combs, we integrate a GTI mirror [25] on the back-facet of theQCL-comb. Extensively used in solid state based mode-locked lasers [35], GTI mirrors are optical cavities specificallydesigned for introducing dispersion. Fig. 2a shows a cross-section of a QCL-comb coated with a GTI mirror takenwith a scanning electron microscope (SEM) and Fig. 2b shows a schematic of the integration of a GTI mirror on aQCL-comb. The GTI mirror is directly deposited on the back-facet of the device and is composed of several layers ofAl2O3 and SiO2 and terminated with a gold layer (see methods and Appendix A). Assuming no absorption is presenton the coating, a GTI mirror usually constitutes a broadband high-reflectivity (HR) coating. In addition, dispersionis introduced as the phase of the reflected light becomes frequency dependent due to the resonance effect introducedby the optical cavity. The dispersion introduced by a GTI is periodic with a period dependent on the length and onthe refractive index of the material. By careful control of these parameters, a GTI mirror can introduce positive ornegative dispersion to the QCL-comb (see Appendix A).

Different types of GTIs were evaporated on the back-facet of several devices. During each evaporation, a InP

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FIG. 3. Dispersion measurements of QCL-combs. a Set-up used to acquire the interferogram generated by the QCL-combbiased below threshold on a FTIR. This interferogram is used to retrieve the relative phase accumulated through a round-tripon the device (see Appendix A). b Relative phase accumulated through a round-trip on the device for a QCL-comb coatedwith a GTI mirror introducing negative dispersion (T = -15 C). c Measurement of the GDD of QCL-combs (T = -15 C).Three different coatings were evaporated on the back-facet of three different devices (4.5 mm long devices cleaved together). dMeasurement of the GDD of QCL-comb as a function of the laser current (T = -15 C).

substrate was coated as a reference sample so the dispersion introduced by the GTI mirror can be characterizedindependently of the device on which it was evaporated. A FTIR was used to measure the complex reflection spectrumof the coating (see Fig. 2c and Appendix A). Fig. 2d shows the measured values of the GDD introduced by the GTImirror, as well as the GDD obtained by simulation (see methods). The typical periodic variations of the GDD of aGTI are observed. Whenever the introduction of negative-dispersion is desired, the GTI can be designed such that oneof its negative resonances lies in the spectral region of the respective QCL-comb. This is depicted on Fig. 2d where wehighlight the part of the spectrum where the comb is operating. At this particular resonance, situated around 1300cm−1, we observe a disagreement between the simulated value of GDD and its measured value. This disagreement isattributed to the fact that SiO2 starts to be absorbing in this spectral region (see Appendix A). This absorption addsa contribution to the total GDD introduced by the GTI. The value introduced at the minimum of this resonance ismeasured to be ' -7000 fs 2 (see inset of Fig. 2d). We also use the same measurement technique for characterizingthe dispersion introduced by a standard HR coating (300 nm of Al2O3, 150 nm of gold). As expected, the GDD of astandard HR coating does not show any resonance effect and does not add any significant dispersion to the device.

B. Dispersion measurements in QCL-combs

For further evaluating the dispersion compensation technique, we also measure the dispersion of QCL-combs afterbeing coated with a GTI mirror. GTI mirrors introducing positive and negative dispersion were evaporated on differentQCL-combs. Particular attention was given to use close to identical devices by using lasers with the same dimensions(ridge width and length) and from the same fabrication process. On the previous section, a QCL-comb coated witha standard HR coating was characterized (see Fig. 1) and we use this device as our reference sample.

The dispersion of QCL-combs is measured by driving the QCL-comb close to but below threshold and acquiringthe interferogram generated by a FTIR, as shown schematically in Fig. 3a. By careful analysis of the interferogram,the relative phase accumulated through a round-trip on the device can be extracted and the GDD of the QCL-combcan therefore be measured (see Appendix A). Fig. 3b shows the relative phase of a device coated with a GTI mirror

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FIG. 4. Dispersion compensated QCL-combs. a Power-current-voltage of a QCL-comb (4.5 mm long, episide-down mountedon AlN submount) coated with a GTI mirror introducing negative dispersion. The measurements are done in CW operationat different temperatures. Single-mode and comb regimes are highlighted. b Electrical RF spectra acquired at T = -10 C fordifferent values of current, measured with a spectrum analyser (span = 200 kHz, RBW = 500 Hz, acquisition time = 20 ms).The RF spectra are centered at 9.814 GHz, corresponding to the RF beatnote created by a 4.5 mm long device. The measuredRF spectra show single and narrow beatnotes (FWHM < 500 Hz). No high-phase noise regime is observed. c Optical spectraacquired at T = -10 C at the same values of current as in Fig. 4b and acquired with a FTIR (0.12 cm−1 resolution). TheQCL-comb spectrum is centered at 1335 cm−1 and spans over 45 cm−1 in the comb regime.

introducing negative dispersion, when the device is biased 2% below threshold. The dispersion of devices coated withdifferent GTI mirrors is shown in Fig. 3c. The determination of the dispersion is limited to the spectral range of theactive region gain bandwidth (typically from 1250 cm−1 to 1460 cm−1), as this method is based on the subthresholdmeasurements (see Appendix A). The QCL-comb coated with a standard HR coating is operating with a total positiveGDD of 4131 fs2 (measured at 1330 cm−1). A similar device coated with a GTI mirror introducing positive GDD

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FIG. 5. High-performance QCL-combs. a Optical spectrum of a high performance QCL-comb (6.0 mm long, GTI mirror onthe back facet introducing negative dispersion) acquired at T = -6 C, I = 1560 mA. The power-per-mode distribution shows anormalized standard deviation of 31 %. b RF spectrum measured at the same value of current than in Fig. 5a, acquired with aspectrum analyzer (span = 50 MHz, RBW = 30 kHz, acquisition time = 20 ms). The RF spectrum shows a narrow beatnote,characteristic of comb operation, together with a pedestal observed at a level 40 dB lower then the carrier. The signal-to-noiseratio of the RF beatnote is more then 40 dB.

shows a total dispersion of 10602 fs2. The difference between the values of GDD of these two devices correspond tothe measured value of the GDD measured in the reference GTI mirror, thus substantiating the claim that the addedGDD is due to the engineered GTI coating. Finally, we also measure the dispersion of the device coated with a GTImirror designed to introduce negative dispersion. This device is operating with a total negative GDD of −3546 fs2.

In order to justify the introduction of the term ∆kgain to the phase-matching condition for QCL-combs, the effectof gain on the dispersion was investigated by measuring the GDD of a QCL-comb as a function of the laser current.The device is always driven below threshold, as the intention is to study the dispersion of the device with no effectof gain clamping. Fig. 3d shows the GDD of the device coated with a GTI mirror introducing negative dispersion fordifferent driving currents (subthreshold measurements). The peak GDD value changes from 2591 fs2 at I = 530 mAto −26 fs2 at I = 770 mA, demonstrating that the effect of gain on the total device dispersion is significant. Therefore,this measurement demonstrates that the gain-induced dispersion has to be considered when designing QCL-combs.

C. Suppression of the high-phase noise regime

We now characterize the performances of QCL-combs where the dispersion was controlled by GTI mirrors. Asshown in Fig. 3c, devices coated with a standard HR coating show small but positive dispersion values. Moreover,devices coated with GTI mirrors introducing positive dispersion showed the same performances as QCL-combs coatedwith standard HR coatings. Therefore, only the devices coated with GTI mirrors introducing negative dispersion areinvestigated here.

The performances of a QCL-comb coated with a GDD mirror introducing negative GDD (−6814 fs2 introducedat 1258 cm−1) is shown in Fig. 4. We use the same characterization set-up as already described in Fig. 1a, whereoptical spectra and RF spectra can be acquired simultaneously. Fig. 4a shows the power-current-voltage measured inCW operation for a GTI-coated QCL-comb with negative dispersion. As GTI mirrors also act as HR coatings, weobserve a decrease of the threshold current as well as an increase of the slope-efficiency. The device emits 142 mW atT = -20 C in CW operation. We observe in the RF spectra (see Fig. 4b) that the beatnotes generated at the combrepetition frequency are extremely narrow (FWHM < 500 Hz) for all the different values of current. Therefore, thecomb regime – which was present over a small range of the dynamical range of the QCL-comb without GTI mirror –is now observed over a large dynamic range of the QCL-comb. More importantly, we observe that the device operatesin the comb regime until the laser roll-over and that no high-phase noise regime is observed. Finally, as observed inthe optical spectra shown in Fig. 4c, the power-per-mode distribution is more homogeneous when compared to theQCL-comb with no dispersion compensation (see Fig. 1c). These findings were observed in several similar devices(same length, same laser fabrication process) which where coated with the same GTI mirror (see Appendix B).

High performances QCL-combs are obtained when compensating the dispersion of a 6 mm long device with a GTImirror introducing negative dispersion (−6814 fs2 introduced at 1258 cm−1). Fig. 5a shows the optical spectrum ofsuch QCL-comb, acquired when the laser is close to roll-over. The RF spectrum is also measured and is shown inFig. 5b. The power-per-mode distribution on the optical spectrum shows a normalized standard deviation of 31 %.More importantly, the RF spectrum shows that the laser is operating in a comb regime, characterized by a singleand narrow RF beatnote (FWHM < 30 kHz). Even though we observe a broad pedestal on the RF spectrum, thispedestal is observed at a level 40 dB lower then the carrier. Moreover, the RF beatnote signal-to-noise ratio (40 dB

8

for the beatnote shown in Fig. 5b) is significantly higher then the ones observed for QCL-combs with a standard HRcoating (see Fig. 1c). Again, no high-phase noise regime was observed on this device.

D. Discussion and conclusion

Our experimental results show that QCL-combs can be precisely designed in order to achieve high-performanceMIR semiconductor based frequency combs. A detailed experimental analysis of the dispersion introduced on QCL-combs is performed and the concept of an integrated GTI mirror for QCL-combs is introduced. These GTI mirrorswere designed in order to introduce positive or negative GDD. Improved designs of GTI mirrors based on differentmaterials (Ge, YF3) could also be implemented in case higher values of dispersion compensation are needed. Byfine characterization of the dispersion introduced by the GTI, QCL-combs operating at negative GDD values wereobtained. This led to QCL-combs showing a comb regime spanning over a wide current range, and no signatureof high-phase noise regime was observed. Moreover, the power-per-mode distribution on these QCL-combs is morehomogeneous compared to previously designed QCL-combs. These devices are ideal for systems using QCL-combs forspectroscopy applications, where a highly inhomogeneous power distribution along the comb modes is detrimental forhigh accuracy spectroscopy, as important values of signal-to-noise ratio are needed over the entire spectrum [22].

In conclusion, we have demonstrated a high-performance MIR QCL-comb obtained by dispersion compensation. Byoperating in the negative dispersion regime, the QCL-comb perfomances were dramatically improved. We achievedhigh power QCL-combs ('150 mW) spanning over ' 70 cm−1, where the comb operation regime is extended over awide current range and where no signature of the high-phase noise regime is observed. The spectral coverage of theQCL-combs is only limited by the bandwidth of the gain medium. Therefore, by using GTI mirrors to compensatethe dispersion of multi-stack QCL designs with broader spectrum, QCL-combs as broad as 300 cm−1 could be inprinciple fabricated. For compensating the dispersion in a wider range, GTI mirrors terminated with dielectric HRcoatings could be realized or double GTI designs could also be implemented [36]. Conversely, the comb structurechanges dramatically when operating in the negative dispersion region, as shown by the increase of the comb operationregime and also by the modification of the power distribution spectrum. This is a signature that the control of thedispersion can induce a change in the phase distribution between the comb modes. By measuring the relative phasesof the comb modes as well as by measuring an ultra-short temporal profile of the laser intensity, by using a frequency-resolved optical gating technique [37] or a ultrafast temporal magnifier [38, 39] – as recently done on the field of Kerrcombs [14, 40] and also for QCL-combs [26] – the structure of a QCL-comb can be fully understood. The control ofthe comb phases could potentially lead to the creation of QCL-combs operating in comb states not observed to date.

I. METHODS

A. QCL-comb characterization

In order to characterize the performance of QCL-combs, the RF spectrum containing the comb repetition frequencyand the optical spectrum have to be acquired simultaneously. The QCL-combs are driven with low noise currentdrivers (Wavelength electronics QCL500 OEM or QCL2000 LAB) with a specified average current noise density of 2

nA/√

Hz. The temperature fluctuations of the lasers were also reduced to less than 10 mK by using a low thermaldrift temperature controller (wavelength electronics PTC10K-CH) with a 50 kΩ thermistor. The comb repetitionfrequency is measured through the RF port of a bias-tee inserted between the current driver and the QCL-comb (c.f.Fig. 1a) [19, 41]. A RF spectrum analyzer (Rhode & Schwarz FSU50) is used to acquire the RF spectrum. Aftercollimation by a high-numerical aperture (0.86) aspheric lens, the QCL-comb output is sent to a Fourier TransformInfrared Spectrometer (FTIR, 0.12 cm−1 resolution) in order to acquire the optical spectrum (c.f. Fig. 1a).

B. GTI mirrors for dispersion compensation

The GTI mirrors designed for our QCL-combs consist of different layers of dieletric materials and a final layer ofgold. Ideally, the layers of the GTI have to be transparent or at least introduce negligible absorption. We thereforeused a combination of Al2O3 and SiO2, as they are relatively transparent in the spectral region of the QCL-combsdesigned for this study (see see Appendix A). The operation of the GTI mirror is done such that either a minimumor maximum of the GDD introduced by the mirror lies in the comb spectral region, in order to introduce negativeor positive dispersion, respectively. The design is performed numerically by using a simulation tool computing thecomplex reflectivity of the coating, based on a transfer matrix formalism. However, the starting point of the design

9

is given by the analytical expression of the GDD introduced by a GTI made with a perfect transparent material

GDDGTI = − 2τ20 (1−Rt)√Rt sinωτ0

(1 +Rt − 2√Rt cosωτ0)2

where τ0 is the cavity roundtrip time, Rt is the reflection coefficient of the low reflectivity facet of the GTI and ωis the optical frequency. We used the transfer matrix simulation tool only to improve and refine this initial design,in which the layered structure and the absorption of the different layers were not considered. The precision of theindividual layer thicknesses is of critical importance for the correction of the dispersion introduced by the GTI mirror.To satisfy the required precision, calibration runs were conducted before every GTI evaporation to ensure variationsof the thicknesses on the order of 3% percent.

END NOTES

ACKNOWLEDGEMENTS

We thank Dr. Andreas Hugi for fruitful discussions. This work was financially supported by the Swiss NationalScience Foundation (SNF200020 - 152962) and by the ETH Pioneer Fellowship programme.

Author Contributions

J.W. designed the QCL active region. M.B grew the QC structure. M.J.S. and G.V fabricated the QCL-combs.G.V. designed the GTI mirrors and S.R. fabricated them. G.V. and J.F. developed the algorithm for retrieving theGDD. D.K. and G.V. mounted the devices and carried out the measurements. G.V. wrote the paper and madethe figures. G.V. and J.F. joined the discussion and provided comments. All the work has been done under J.F.supervision.

Competing financial interests

The authors declare no competing financial interests.

Appendix A: Dispersion characterization of QCL-combs

In this section, we describe the procedure to measure the dispersion introduced by GTI mirrors as well as thedispersion of a QCL-comb. We first describe the entire procedure for the case of GTI mirrors. The method employedfor the dispersion measurement of QCL-combs being very similar, only the differences will be detailed.

For each evaporation of a GTI mirror, a InP substrate (320 µm thick) is placed on the evaporation chamber andis used as a reference sample. This reference sample is used to characterize the dispersion introduced by the GTImirror. The characterization is done by placing the device under test (DUT) after the beam-splitter on a FTIR,where the beams are recombined, as shown schematicaly on Fig. 2c of the main text. An interferogram generated bythe reflection upon the GTI mirror is then acquired. A typical interferogram is shown in Fig. 6a, where we observean intense center burst, corresponding to the position of the moving mirror where both arms are introducing thesame optical delay. More importantly, several small satellites are also observed, indicated by the red dots on Fig. 6a.As explained schematically on Fig. 2b of the main text, these different satellites correspond to the case where lightexperience multiple roundtrips on the GTI mirror. The first and most intense satelite (position 14000 in Fig. 6a)corresponds to the case of a single roundtrip and contains the information concerning the dispersion introduced bythe GTI.

In order to calculate the dispersion introduced by the GTI, the first satellite is numerically isolated and apodized,as shown in Fig. 6b. The length of this interferogram has to be carfully chosen, as it determines the spectral resolutionas well as the accuracy of the GDD measurement [42]. After apodization, we perform a fourier transform (Fast FourierTransform algorithm) and compute the phase spectrum, which is shown in Fig. 6c. This phase corresponds to theaccumulated phase when light experiences a roundtrip inside the GTI mirror, as shown schematically in Fig. 2b ofthe main text. Finally, as the group delay dispersion (GDD) is defined as

10

Position (a.u.)-1500 -1000 -500 0 500 1000 1500

Inte

nsity

(a.u

.)

-2.5-2

-1.5-1

-0.50

0.51

1.52

2.5

500 1000 1500 2000 2500 3000 3500 40000

0.5

1

1.5

2Al2O3SiO2

Position (a.u.)0 5000 10000 15000 20000 25000

Intn

sity

(a.u

.)

-8-6-4-202468

1012

Wavenumber (cm-1)500 1000 1500 2000 2500 3000 3500 4000

68

1012141618202224

(rad

)

Wavenumber (cm-1)

a) b)

Extin

ctio

n co

effic

ient

Comb operationregion

c) d)

FIG. 6. Method for dispersion characterization of GTI mirrors as well as QCL-combs. a Interferogram generated by a FTIRwhen measuring the reflection of a GTI mirror. The red dots correspond to the different satellites observed on the interferogram.The resolution is set to 1.7 cm−1, enough to be able to observe up to the second satellite created on the interferogram. b Zoomon the first satellite, where the dispersion information is contained. The number of points of this isolated interferogram setsthe frequency resolution of the GDD measurement as well as the GDD accuracy. c Relative phase spectrum extracted from thefirst satellite of the interferogram. d Extinction coefficient of the dielectric materials (Al2O3 and SiO2) used in GTI mirrorsdesigned for QCL-combs. The comb spectral region is also highlighted.

∆φ(ω) = ∆φ0︸︷︷︸absolute phase at ω0

+(ω − ω0)

(d∆φ

dω

)ω0︸ ︷︷ ︸

Group Delay

+1

2(ω − ω0)2

(d2∆φ

dω2

)ω0︸ ︷︷ ︸

GDD

the GDD can be obtained by computing the second derivative of the relative phase ∆φ according to ω. Themeasured GDD is displayed on Fig. 2c of the main text.

We report now the different designs of GTI mirrors that were used to introduce positive/negative values of dispersion,as described in the main text. Table I shows the detailed structure of the different designs of GTI mirrors. The GTImirrors are composed of different layers of Al2O3 and SiO2 and are always terminated with a thin layer of gold. Asdiscussed in the main text, a discrepancy between the simulated values of the GDD introduced by a GTI mirro and themeasured values of the GDD is observed around 1270 cm−1. This is explained by the absorption introduced by SiO2.Fig. 6d shows the extinction coefficient of both Al2O3 and SiO2 as well the spectral region were the comb is operating.Although Al2O3 can be assumed perfectly transparent in the comb operation region, SiO2 is slightly absorbing in thisspectral region. This small absorption introduces an additional term to the relative phase ∆φ introduced by the GTI,which directly translates into an additional source of dispersion. By using this additional source of GDD, we wereable to introduce around -7000 fs2 at 1270 cm−1, value that was not possible to achieve with a totally transparentGTI mirror with the same thickness.

Finally, we described the method used for characterizing the dispersion of MIR QCL-combs. The QCL-comb isdriven under threshold and is aligned to a FTIR, which is used to acquire an interferogram. The first satellite observedin the interferogram corresponds to the relative phase between the light being directly emitted by one facet and thelight experiencing a roundtrip into the cavity and subsequently emitted by this same facet [43]. Therefore, theinformation concerning the dispersion of a QCL-comb is contained into this part of the interferogram. By applyingthe same numerical method discribed for the analysis of the dispersion introduced by GTI mirrors, the phase spectrumas well as the GDD of a QCL-comb can be computed. The GDD of a QCL-comb coated with a GTI mirror is shownin Fig.3 c of the main text.

11

GTI structure for positive GDD GTI structure for negative GDD

Material Thickness Material Thickness

Al2O3 250 nm Al2O3 511 nm

SiO2 250 nm SiO2 102 nm

Al2O3 250 nm Al2O3 511 nm

SiO2 250 nm SiO2 102 nm

Al2O3 250 nm Al2O3 511 nm

SiO2 250 nm SiO2 102 nm

Al2O3 250 nm Al2O3 511 nm

SiO2 250 nm SiO2 102 nm

Al2O3 250 nm Al2O3 511 nm

SiO2 250 nm SiO2 102 nm

Al2O3 150 nm Al2O3 154 nm

Au 150 nm Au 154 nm

TABLE I. Detailed structure of GTI mirrors developed for dispersion compensation of QCL-combs. The first evaporated layercorrespond to the first layer of the table.

Appendix B: Additional QCL-comb with negative GTI mirror

In this section, we show additional data concerning QCL-combs coated with GTI mirrors introducing negativedispersion. We fabricated several devices with the same length from the same laser fabrication process. The samedesign of GTI mirror introducing negative dispersion was used for all the evaporations. The device shown in thissection is similar to the device shown on section C of the main text (same process, cleaved at the same time) but differsby the fact that the GTI mirror was coated on a different evaporation run. The device operates at room-temperatureemitting > 100 mW of output power in CW operation (see Fig. 7a). No high-phase noise regime is observed forthis device, as observed for the device described on the section C of the main text. The device shows single narrowRF beatnotes over the entire current range where multimode operation is observed (see Fig. 7a for the RF spectraand Fig. 7b for the optical spectra as a function of current at a fixed temperature), characteristic of comb regimeoperation.

12

16

14

12

10

8

6

4

2

Volta

ge (V

)

700600500400300200100Current (mA)

140

120

100

80

60

40

20

0

Power (m

W)

c)b)

a)

I = 580 mA

I = 602 mA

I = 620 mA

I = 660 mA

I = 680 mA

I = 700 mA

I = 743 mA

Inte

nsity

(a.u

.)

40

30

20

10

0

14001380136013401320Wavenumber (cm-1)

60

40

20

0

12

8

4

0

25201510

50

15

10

5

0

12

8

4

0

25

20

15

10

5

0

CW, T = -16 0CGTI coatedL = 4.5 mm

-120

-110

-100

-20 -10 0 10 20Frequency (MHz)

-120

-110

-100

-90-120

-110

-100

-90-120

-110

-100

-90

-120

-110

-100

-90

-120

-110

-100

-90

-120

-110

-100

I = 580 mA

I = 602 mA

I = 620 mA

I = 660 mA

I = 680 mA

I = 700 mA

I = 743 mA

Elec

tric

al P

ower

(dBm

)

Span = 50 MHzRBW = 30 kHz

CW, T = -16 0CGTI coatedL = 4.5 mm

CWGTI coatedL = 4.5 mm

Comb regime

Single-mode regime

-20 C -10 C 0 C 10 C 20 C

FIG. 7. Dispersion compensated QCL-combs (additional data). a Power-current-voltage of a QCL-comb (4.5 mm long,episide-down mounted on AlN submount) coated with a GTI mirror introducing negative dispersion. The measurements aredone in CW operation at different temperatures. Single-mode and Comb regimes are highlighted are highlighted. b ElectricalRF spectra acquired at T = -16 C at different values of current, measured with a spectrum analyser (span = 50 MHz, RBW= 300 kHz, acquisition time = 20 ms). The RF spectra are centered at 9.814 GHz, corresponding to the RF beatnote createdby a 4.5 mm long device. The measured RF spectra show single and narrow beatnotes (FWHM < 30 kHz). No high-phasenoise regime is observed. c Optical spectra acquired at T = -16 C at the same values of current as in Fig. 7b and acquiredwith a FTIR (0.12 cm−1 resolution). The QCL-comb spectrum is centered at 1360 cm−1 and spans over 50 cm−1 in the combregime.

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